How to Use Area Models to Multiply One-Digit Numbers By Two-digit Numbers

An area model multiplies a one-digit number by a two-digit number by splitting the two-digit number into tens and ones, multiplying each part separately, and adding the two areas. Below: how to draw and label the rectangle, and worked examples.

A Step-by-step Guide to Using Area Models to Multiply One-Digit Numbers By Two-digit Numbers

Using area models to multiply one-digit numbers by two-digit numbers can help students visualize the multiplication process. Here’s a step-by-step guide using the example \(5 x 12\).

Step 1: Draw the Area Model

Start by drawing a large rectangle. This rectangle will represent the entire multiplication problem.

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Step 2: Divide the Rectangle

Next, divide the rectangle into two parts. This is because we’re multiplying by a two-digit number (12). The larger part represents the tens place (10), and the smaller part represents the ones place (2). Label each section.

It would look something like this:

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| 10 | 2 |
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Step 3: Write the One-Digit Number

On the side of the rectangle, write the one-digit number you’re multiplying (5).

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5 | 10 | 2 | -----------------

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Step 4: Calculate the Area

The area of a rectangle is found by multiplying its length by its width. So, multiply the one-digit number (5) by each part of the two-digit number (10 and 2).

For the first part of the rectangle: \(5 x 10 = 50\)
For the second part of the rectangle: \(5 x 2 = 10\)

Write these products inside the respective parts of the rectangle.

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5 | 50 | 10 | -----------------

Step 5: Add the Areas

Finally, add the two areas together. In this case, \(50 + 10 = 60\).
So, \(5 x 12 = 60\).
Area models are a great way for students to visualize multiplication, breaking down complex problems into simpler, more manageable parts. It’s especially useful for students who are visual learners.

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